
462 Optical Fiber Communication Systems with MATLAB
®
and Simulink
®
Models
orthogonality between the two frequency modulated signals [10,19,28]. The base-band rep-
resentation of an optical MSK pulse train x(t) at the nth symbol interval is expressed by [10]
x t
E
T
e nT T t nT T
b
j t a
n
( )
( , )
= − ≤ ≤ +
Φ
/ /2 2 (11.9)
where E
b
is the bit energy. The phase term, Φ
n
(t,a), is given by
Φ
n k
k
n
d n
n
t a a f t T nT a
t a
( , ) ( )
( , )
=
+ + −
= +
=−∞
−
−
∑
π π
θ
/ /2 2 2
2
1
1
ππf t T nT a
d n
( )+ −/2
(11.10)
where a
n
∈ {+1, −1} is the data logics transmitted at the nth interval.
Equation 11.10 shows that the MSK phase evolution follows a linear phase trellis.
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